Rank Minimization with Structured Data Patterns
Paper in proceedings, 2014

The problem of finding a low rank approximation of a given measurement matrix is of key interest in computer vision. If all the elements of the measurement matrix are available, the problem can be solved using factorization. However, in the case of missing data no satisfactory solution exists. Recent approaches replace the rank term with the weaker (but convex) nuclear norm. In this paper we show that this heuristic works poorly on problems where the locations of the missing entries are highly correlated and structured which is a common situation in many applications. Our main contribution is the derivation of a much stronger convex relaxation that takes into account not only the rank function but also the data. We propose an algorithm which uses this relaxation to solve the rank approximation problem on matrices where the given measurements can be organized into overlapping blocks without missing data. The algorithm is computationally efficient and we have applied it to several classical problems including structure from motion and linear shape basis estimation. We demonstrate on both real and synthetic data that it outperforms state-of-the-art alternatives.

Author

Viktor Larsson

Lund University

Carl Olsson

Lund University

Erik Bylow

Lund University

Fredrik Kahl

Chalmers, Signals and Systems, Signalbehandling och medicinsk teknik, Imaging and Image Analysis

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

03029743 (ISSN) 16113349 (eISSN)

Vol. 8691 PART 3 250-265

Subject Categories

Computer Vision and Robotics (Autonomous Systems)

Medical Image Processing

DOI

10.1007/978-3-319-10578-9_17

ISBN

978-331910577-2

More information

Latest update

3/2/2018 9